A1 Refereed original research article in a scientific journal
On Quasimöbius Maps in Real Banach Spaces
Authors: M Huang, Y Li, M Vuorinen, X Wang
Publisher: HEBREW UNIV MAGNES PRESS
Publishing place: JERUSALEM; PO BOX 39099, JERUSALEM 91390, ISRAEL
Publication year: 2013
Journal: Israel Journal of Mathematics
Journal name in source: Israel Journal of Mathematics
Journal acronym: Isr.J.Math.
Number in series: 1
Volume: 198
Issue: 1
First page : 467
Last page: 486
Number of pages: 20
ISSN: 0021-2172
DOI: https://doi.org/10.1007/s11856-013-0043-6
Web address : http://api.elsevier.com/content/abstract/scopus_id:84883821449
Abstract
Suppose that E and E' denote real Banach spaces with dimension at least 2, that D not subset of E and D' not subset of E' are domains, that f : D -> D' is an (M, C)-CQH homeomorphism, and that D is uniform. The aim of this paper is to prove that D' is a uniform domain if and only if f extends to a homeomorphism (f) over bar : (D) over bar -> (D) over bar' and (f) over bar is eta-QM relative to partial derivative D. This result shows that the answer to one of the open problems raised by Vaisala from 1991 is affirmative.
Suppose that E and E' denote real Banach spaces with dimension at least 2, that D not subset of E and D' not subset of E' are domains, that f : D -> D' is an (M, C)-CQH homeomorphism, and that D is uniform. The aim of this paper is to prove that D' is a uniform domain if and only if f extends to a homeomorphism (f) over bar : (D) over bar -> (D) over bar' and (f) over bar is eta-QM relative to partial derivative D. This result shows that the answer to one of the open problems raised by Vaisala from 1991 is affirmative.
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